Marching on in time (MOT)-based time domain integral equation (TDIE) solvers provide an appealing avenue for analyzing transient electromagnetic interactions with large and complex structures. Unfortunately, these solvers often suffer from temporal (low-frequency) and spatial (dense-mesh) breakdown phenomena when applied to the analysis of low- to medium-frequency electromagnetic transients on geometrically intricate and multiscale structures, thereby preventing their application to many important scientific and engineering problems. This project seeks the development of new plane wave time domain-accelerated, regularized MOT-TDIE solvers that are immune to temporal and spatial breakdown phenomena. The proposed techniques eliminate temporal and spatial breakdown phenomena in MOT-TDIE solvers by leveraging hierarchical basis functions and new time domain Calderon identities, respectively. In addition, they guaranty low-frequency stability in MOT-TDIE solvers by exploiting the spectral properties of the Calderon regularizer. MOT-TDIE solvers resulting from this effort will permit the fast analysis of low- to medium-frequency electromagnetic transients on geometrically intricate and mixed-scale structures. The educational objective of this project is to develop a comprehensive set of educational materials supporting a course covering all aspects of fast MOT-TDIE technology and to use them in teaching and outreach.

The development of fast and higher-order accurate MOT-TDIE solvers that robustly and seamlessly apply across spatial and temporal scales will permit the analysis of a wide class of scientific and real-world electromagnetic engineering problems that are intractable using present day methods. Given their grid-robust nature, the electromagnetic simulators resulting from this effort will permit optical scientists to rigorously analyze transient effects in nonlinear and disordered metamaterials and nanostructures without resorting to homogenization approximations, thereby creating a new avenue for controlling and directing the flow and electromagnetic waves and light in fibers and on chips. In addition, they will allow electronic engineers to design digital integrated circuits and RF wireless sensors without resorting to ad-hoc spatial decomposition methods, thereby resulting in significant savings in development time and costs. And finally, they will permit automotive and aerospace engineers to appropriately protect their designs from unwanted electromagnetic interference, thereby improving safety and impacting national security by reducing the threat of remotely generated system upsets.